If A = (1, 0, 0) and B = (0, 1, 0), what is the vector product A × B?

If A = (1, 0, 0) and B = (0, 1, 0), what is the vector product A × B?

Correct Answer: (0, 0, 1)

Step 1: Identify the vectors A and B. A = (1, 0, 0) and B = (0, 1, 0).
Step 2: Write down the formula for the vector product (cross product) A × B.
Step 3: Use the determinant method to calculate the cross product. Set up a 3x3 matrix with unit vectors i, j, k in the first row, components of A in the second row, and components of B in the third row.
Step 4: The matrix looks like this: | i j k |
Step 5: Fill in the second row with A's components: | 1 0 0 |
Step 6: Fill in the third row with B's components: | 0 1 0 |
Step 7: Calculate the determinant of this matrix to find A × B.
Step 8: The determinant gives you the vector (0, 0, 1).
Step 9: Confirm the result using the right-hand rule: point your fingers in the direction of A, curl them towards B, and your thumb points in the direction of the result.

Vector Product – The vector product (or cross product) of two vectors results in a vector that is perpendicular to both original vectors, calculated using the right-hand rule.
Right-Hand Rule – A method used to determine the direction of the resulting vector in a cross product, where the thumb points in the direction of the first vector and the fingers curl towards the second vector.